Paper Info
Title
Capture Zones Of The Family Of Functions Lambda Z(M) Exp(Z)
Abstract
We consider the family of entire transcendental maps given by F-lambda,F-m (z) = lambdaz(m) exp(z) where m greater than or equal to 2. All functions F-lambda,F-m have a superattracting fixed point at z = 0, and a critical point at z = -m. In the dynamical plane we study the topology of the basin of attraction of z = 0. In the parameter plane we focus on the capture behavior, i.e. lambda values such that the critical point belongs to the basin of attraction of z = 0. In particular, we find a capture zone for which this basin has a unique connected component, whose boundary is then nonlocally connected. However, there are parameter values for which the boundary of the immediate basin of z = 0 is a quasicircle.
Year
DOI
Venue
2003
10.1142/S0218127403008120
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
Field
DocType
iteration, entire functions, Julia set, Fatou set, polynomial-like mappings, locally connected set
Entire function,Mathematical analysis,Critical point (thermodynamics),Quasicircle,Julia set,Connected component,Transcendental number,Fixed point,Mathematics
Journal
Volume
Issue
ISSN
13
9
0218-1274
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Núria Fagella100.68
Antonio Garijo222.23